Finite Group Databasebeta

← #25137935

Subgroups — #25137935

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583177C211yesmaximal, characteristic, complemented
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19140420C211yesmaximal, characteristic, complemented
4#19137290C211yesmaximal, characteristic
5#19136023C211yesmaximal, characteristic, complemented
6#19136021C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic
8#19135541C211yesmaximal, characteristic, complemented
9#19135364C211yesmaximal, characteristic, complemented
10#19135339C211yesmaximal, characteristic, complemented
11#19135327C211yesmaximal, characteristic, complemented
12#19135289C211yesmaximal, characteristic, complemented
13#19135280C211yesmaximal, characteristic, complemented
14#19134603C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#14583177—24no—
20#14582957—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582841—21no—
32#14582835—21no—
33#14582820—21no—
34#14582811—21no—
35#14582802—21no—
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582792—21no—
41#14582779—21no—
42#14582774—21no—
43#14582764C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69#13063284—22no—
70#13063284—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063258—22no—
93#13063258—22no—
94Dic43⋊C8—22no—
95Dic43⋊C8D414yescomplemented
96#13063246—22no—
97#13063246—22no—
98C22⋊(C43⋊C8)—22no—
99#13063235—22no—
100C8×Dic43—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#121×C43—22no—
115#121×C43—22no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#106×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124C22⋊C8×C43—22no—
125#95×C43—21no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C2×D4×C43—24no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—81no—
135C2×D4×C43—81no—
136C2×D4×C43#4112yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—42no—
153C22×Dic43—81no—
154C22×Dic43—81no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×Dic86—42no—
160C2×Dic86—81no—
161C2×Dic86—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D412yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43#4112yes—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—81no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—42no—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—81no—
194C4⋊Dic43—81no—
195Dic43⋊C4—42no—
196Dic43⋊C4—81no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C4×Dic43C2×D412yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C2×D412yes—
208C23×C43—21no—
209C23×C43—22no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C22×D411yescharacteristic
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—84no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—84no—
273C2×Dic43#12112yes—
274C2×Dic43#12112yes—
275Dic86—84no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280#24712—431nomaximal, Sylow
281C22×C43—41no—
282C22×C43—42no—
283C22×C43—41no—
284C22×C43—42no—
285C22×C43—41no—
286C22×C43—42no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#53611yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57711yescharacteristic
301C22×C43#57811yescharacteristic
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43#54711yescharacteristic
307C4×C43#54811yescharacteristic
308C4×C43#55211yescharacteristic
309C4×C43#55611yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#474—431no—
319C2×#433—431no—
320#2628—431no—
321#2324—431no—
322#2076—431no—
323#2075—431no—
324#2034D4311yescharacteristic
325#2033—431no—
326#1987—431no—
327#1949—431no—
328#1944—431no—
329#1942—431no—
330#1936—431no—
331#1934—431no—
332#1804—431no—
333C2×C43—81no—
334C2×C43—82no—
335C2×C43#241511yescharacteristic
336C2×C43#305811yescharacteristic
337C2×C43#306311yescharacteristic
338C2×C43#311811yescharacteristic
339C2×C43#312411yescharacteristic
340C2×C43#324111yescharacteristic
341C2×C43#324311yescharacteristic
342C2×C4⋊Q8—431no—
343C2×#121C2×D4311yescharacteristic
344C2×C4×D4—431no—
345C2×#117—431no—
346#474—864no—
347#433—864no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#106C2×D4311yescharacteristic
352C2×C4⋊C8—431no—
353C2×C4⋊C8—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×C22⋊C8—431no—
359C2×C22⋊C8C2×D4311yescharacteristic
360C2×#97—431no—
361C2×C4×C8—431no—
362#400—861no—
363#399—861no—
364#395—861no—
365#393—861no—
366#390—431no—
367#390—861no—
368#389—431no—
369#389—431no—
370#389—431no—
371#388—861no—
372#386—861no—
373#385—861no—
374#382—431no—
375#380—431no—
376#380—431no—
377#380C2×D4311yescharacteristic
378C4×C4⋊C4—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387C43#2471211yescharacteristic, complemented, Sylow
388C22×Q8—861no—
389C22×D4—21no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—862no—
398C4⋊Q8—862no—
399#121—22no—
400#121—22no—
401C4×D4—862no—
402C4×D4—862no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—431no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—861no—
430#107—862no—
431#107—862no—
432#107—862no—
433#106—22no—
434C4⋊C8—434no—
435C4⋊C8—862no—
436#102—22no—
437#102—22no—
438#102—862no—
439#102—862no—
440C22⋊C8—22no—
441C22⋊C8—862no—
442#97—862no—
443C4×C8—862no—
444#95—21no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—21no—
454C24D4×D4311yescharacteristic
455C2×Q8—3441no—
456C2×Q8—3441no—
457C2×Q8—1722no—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4#1062190012yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—1722no—
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8D4×D4312yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—1722no—
520C4⋊C4#1062190012yes—
521C22⋊C4—24no—
522C22⋊C4—81no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C42—432no—
531C42—432no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C23—21no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C2×D4×D4311yescharacteristic
550Q8—3444no—
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—84no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—3444no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062190011yescharacteristic
601C2×C4#1306337211yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—22no—
604C8—41no—
605C8—862no—
606C8—1721no—
607C22—41no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22#121×D4311yescharacteristic
622C22#1458340511yescharacteristic
623C22#1458347111yescharacteristic
624C22#1458370311yescharacteristic
625C22#1458370311yescharacteristic
626C22#1458370511yescharacteristic
627C22#1458371311yescharacteristic
628C4—42no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—862no—
633C4—862no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—1721no—
639C4—1721no—
640C4#1458354911yescharacteristic
641C4#1458355511yescharacteristic
642C4#1458358611yescharacteristic
643C4#1458361811yescharacteristic
644C2—81no—
645C2—82no—
646C2#1913801711yescharacteristic
647C2#1914424111yescharacteristic
648C2#1914427911yescharacteristic
649C2#1914478011yescharacteristic
650C2#1914485011yescharacteristic
651C2#1914585211yescharacteristic
652C2#1914587611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#24712
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583177C2semidirect
2. C2×#14582957C2semidirect
3. #19140420C2semidirect
5. #19136023C2semidirect
6. #19136021C2semidirect
8. #19135541C2semidirect
9. #19135364C2semidirect
10. #19135339C2semidirect
11. #19135327C2semidirect
12. #19135289C2semidirect
13. #19135280C2semidirect
14. #19134603C2semidirect
95. Dic43⋊C8D4semidirect
387. C43#24712semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831772
C2×#145829572
#191404202
#191372902
#191360232
#191360212
#191357742
#191355412
#191353642
#191353392
#191353272
#191352892
#191352802
#191346032
C43×#20342
#2471243